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Plate Folding, Birthdays, and Thanksgiving

Welcome to this week’s Math Munch!

Icosahedron made from 4 paper plates. Click for instructions.

Big news this week, but first let’s have a look at some construction projects you can easily do at home using paper plates, paper clips, and some tape. They come to us from wholemovement.com, the website of Bradford Hansen-Smith. It’s not a stretch to say that Bradford is kind of cuckoo for circles, as you can probably tell form this introductory video. Naturally, the website is all about the amazing things you can do and learn from folding circles. Check out his gallery and you’ll see what I mean. Using these instructions and 4 paper plates I made the sculptures in these pictures. Above is an icosahedron with 4 of the 20 triangles left as empty space, and down below you can see the cuboctahedron of sorts. There’s even an instruction video for this one. So grab some cheap plates, fold ’em up, experiment, and send us your pictures.

square face view

triangular face view

Born 11.14.12

OK, now for the big news. Last Wednesday, my daughter was born!!! I’m so so so happy.  In honor of Nora’s 0th birthday (you turn 1 on your 1st birthday, right?), let’s check out some birthday math. Here’s a cool little birthday number trick I found. It’s sort of magical, but it actually works because that tangle of arithmetic actually just multiplies the month by 10,000, the day by 100, and adds those together with the year. Hopefully you can see how this much simpler version works.

Here’s a well-known birthday problem: How many people need to be in a room before it’s likely that two of them share a birthday? If there’s 400 people in a room, then there’s definitely a birthday match, but if there’s 300 it’s almost certain as well. What’s the smallest crowd so that the probability of a match birthday is over 50%? For the answer and analysis, check out this Numberphile video on the subject featuring James Grime or this New York Times article, by Steven Strogatz, a wonderful mathematician and author.

Both of these solutions are actually wrong!  That’s because they make the false assumptions that each day has the same likelihood of being someone’s birthday.  You can see in the graphs above that that’s not true at all! On the left, look how dark the summer months are, and look at how gray the days are around Thanksgiving and Christmas. You can click on the left image for an interactive version, or click on the right for more graphs and analysis.

A Thanksgiving Pie Chart

Finally, I’m incredibly excited for Thanksgiving (my very favorite holiday), and in that spirit, I want to take a few lines to say “thank you” to you, dear reader. THANK YOU! Whether you’re a weekly muncher or a first time reader, it’s great to know you’re out there enjoying the math we share.

Obviously of course, Thanksgiving is also about the food. Delicious delicious food. Yummmmm! So, Vi Hart is making a series of Thanksgiving themed videos to showcase the math of the meal. Enjoy the videos, but be careful. You may get terribly hungry.

Happy Thanksgiving and bon appetit!